REACH: Realistic Extension Algorithm via Covariance Hessian

Coarse graining of protein interactions provides a means of simulating large biological systems. Here, a coarse-graining method, REACH, is introduced, in which the force constants of a residue-scale elastic network model are calculated from the variance-covariance matrix obtained from atomistic molecular dynamics (MD) simulation. In test calculations the C α-atoms variance-covariance matrices are calculated from the ensembles of 1-ns atomistic MD trajectories in monomeric and dimeric myoglobin, and used to derive coarse-grained force constants for the local and nonbonded interactions. Construction of analytical model functions of the distance-dependence of the inter-residue force constants allows rapid calculation of the REACH normal modes. The model force constants from monomeric and dimeric myoglobin are found to be similar in magnitude to each other. The MD intra-and intermolecular mean-square fluctuations and the vibrational density of states are well reproduced by the residue-scale REACH normal modes without requiring rescaling of the force constant parameters. The temperature-dependence of the myoglobin REACH force constants reveal that the dynamical transition in protein internal fluctuations arises principally from softening of the elasticity in the nonlocal interactions. The REACH method is found to be a reliable way of determining spatiotemporal protein motion without the need for expensive computations of long atomistic MD simulations.